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TECHNICAL PAPERS

A Linear Material Model for Fiber-Induced Anisotropy of the Anulus Fibrosus

[+] Author and Article Information
Dawn M. Elliott, Lori A. Setton

Department of Biomedical Engineering, Duke University, Durham, NC 27708

J Biomech Eng 122(2), 173-179 (Oct 18, 1999) (7 pages) doi:10.1115/1.429639 History: Received September 13, 1999; Revised October 18, 1999
Copyright © 2000 by ASME
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References

Figures

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Schematic of the intervertebral disc. Collagen fiber angles change with alternating lamellae in the anulus fibrosus. AF=anulus fibrosus, NP=nucleus pulposus. Unit vectors a and b denote orientation of collagen fiber populations in the x1−x2 plane.
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Coordinate system used in model development. Unit vectors a and b denote orientation of collagen fiber populations in the x1−x2 plane. The fiber populations are oriented at an angle θ from the global coordinate system and at an angle 2ϕ from each other.
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Model prediction for modulus in the x1 direction for changing fiber angle, ϕ. Data 1 from 8, data 2 from 9, and data 3 from 37.
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Schematic of fiber populations for several orientations of fiber populations: (A) Physiologic representation of AF fiber populations was used to determine the material property set, θ=0 deg and ϕ=30 deg. (B) Fiber angle ϕ=60 deg for θ=0 deg; alternatively, may represent a coordinate rotation to θ=90 deg while maintaining a physiologic angle ϕ=30 deg. (C) For ϕ=90 deg, the fiber populations coincide and represent the case of transverse isotropy, with the material properties in the x1 direction being transverse to the fiber populations. (D) For ϕ=0 deg, the fiber populations coincide and represent transverse isotropy, with the material properties in x1 direction being in the fiber direction.
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Model prediction for dilatation for a multiple lamella AF at ϕ=30 deg under uniaxial strain in the x1 direction (circumferential) and for a single lamella under uniaxial strain in the fiber direction
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Model prediction for dilatation for a uniaxial strain of 0.1 in the x1 direction as a function of fiber angle, ϕ

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